Find the value(s) of the constant k that makes the following function continuous at x = 3. Show all CALCULUS work!! (5 points) f(x)= k² - kx, In (x-2)+ 10 )
if x <3, if x _>3
Answers
To make the function f(x) = k^2 - kx * ln(x - 2) + 10 continuous at x = 3, we need to ensure that the left and right limits of the function at x = 3 are equal. First, let's calculate the left-hand limit:
lim (x→3-) f(x) = lim (x→3-) (k^2 - kx * ln(x - 2) + 10)
= k^2 - 3k * ln(3 - 2) + 10
= k^2 - 3k + 10
Next, let's calculate the right-hand limit:
lim (x→3+) f(x) = lim (x→3+) (k^2 - kx * ln(x - 2) + 10)
= k^2 - 3k * ln(3 - 2) + 10
= k^2 - 3k + 10
Since we want the function to be continuous at x = 3, the left-hand limit and the right-hand limit must be equal:
k^2 - 3k + 10 = k^2 - 3k + 10
This equation holds for any value of k. Therefore, there are infinite values of k that make the function continuous at x = 3.
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Related Questions
The point-slope form of the equation of a line that passes through points (8, 4) and (0, 2) is y - 4 = 1/4(x - 8). What
iS the slope-intercept form of the equation for this line?
O y = 1/4x- 12
O y= 1/4x-4
O y= 1/4x+2
O y= 1/4x+6
Answers
Answer:
3rd option
Step-by-step explanation:
The equation of a line in point slope form is
y - b = m(x - a)
where m is the slope and (a, b ) a point on the line
Given
y - 4 = \(\frac{1}{4}\) (x - 8)
with m = \(\frac{1}{4}\) and (a, b) = (8, 4 )
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept ) , then
y = \(\frac{1}{4}\) x + c ← is the partial equation
To find c substitute (8, 4) into the partial equation
4 = 2 + c ⇒ c = 4 - 2 = 2
y = \(\frac{1}{4}\) x + 2 ← equation in slope- intercept form
Sarah paid $27.50 for two T-shirts. Each T-shirt cost the same. Let an equal the cost of one new shirt. Create an equation that can be used to find the cost, in dollars, of an shirts. What is the cost of one shirt
Answers
Answer:
x/y, the cost would be $13.75
Step-by-step explanation:
x would be the amount paid and y would be the number of shirts bought.
Answer:
13.75
Step-by-step explanation:
the continuous compounding of interest in a bank leads to the formula A(t)=re^(A0t) for the total amount in the account at time t, where r is the interest rate and A0 is the principal amount
Answers
Answer:The continuous compounding of interest in a bank leads to the formula A(t) = A0 * e^(rt) for the total amount in the account at time t, where r is the interest rate, A0 is the principal amount, and e is the base of the natural logarithm (approximately 2.71828).
Step-by-step explanation:
1. A0 represents the initial principal amount, which is the starting balance of the account.
2. r is the interest rate, expressed as a decimal (e.g., 0.05 for 5% interest rate).
3. t is the time, typically measured in years.
4. e is the base of the natural logarithm (approximately 2.71828).
5. The exponent rt represents the product of the interest rate (r) and the time (t).
6. A(t) represents the total amount in the account at time t, including both the principal and the interest earned.
By continuously compounding interest, the account balance grows at an exponential rate, and the formula A(t) = A0 * e^(rt) is used to calculate the account balance at any given time t.
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Currently you have two credit cards, h and i. Card h has a balance of $1,186. 44 and an interest rate of 14. 74%, compounded annually. Card i has a balance of $1,522. 16 and an interest rate of 12. 05%, compounded monthly. Assuming that you make no purchases and no payments with either card, after three years, which card’s balance will have increased by more, and how much greater will that increase be?.
Answers
The balance increase for card i is $89.24 greater than the balance increase for card h. Card i has a balance of $1,522.16 and an interest rate of 12.05%, compounded monthly. Now, we can calculate the balance for both cards after three years using the compound interest formula: A = P(1 + r/n)^(nt)
Given, Card h has a balance of $1,186.44 and an interest rate of 14.74%, compounded annually.
Card i has a balance of $1,522.16 and an interest rate of 12.05%, compounded monthly. Now, we can calculate the balance for both cards after three years using the compound interest formula: A = P(1 + r/n)^(nt),
where A = final amount, P = principal (initial balance), r = annual interest rate (as a decimal), n = number of times compounded per year, t = time (in years)
For card h,
A = 1186.44(1 + 0.1474/1)^(1*3)
A = 1883.99
For card i, A = 1522.16(1 + 0.1205/12)^(12*3)
A = 1973.23
Therefore, the balance for card i will have increased more than that of card h, and the difference in the increase is: 1973.23 - 1883.99 = 89.24
The balance increase for card i is $89.24 greater than the balance increase for card h. Hence, the required answer is card i.
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help me with this question please
Answers
Based on the truth table constructed above, since they are not the same. Then the two sattements are not equivalent.
Use the given area A of the rectangle to find the value of x . A rectangle with its length labeled left-parenthesis 4 x plus 3 right-parenthesis feet and width labeled left-parenthesis 4 x minus 5 right-parenthesis feet. The area of the rectangle is 209 square feet.
Answers
Answer:
x = 4
Step-by-step explanation:
Length = (4x + 3) feet
Width = (4x - 5 )feet
Area = Length x Breadth
209 = (4x + 3)(4x - 5)
209 = 4x( 4x -5) + 3 (4x -5)
\(209 = 16x^2 -20x +12x -15\\\\0 = 16x^2 -8x -15 -209\\\\16x^2 -8x -224 = 0\)
\(Quadratic \ Equation \ with a = 16, b = -8, c = -224 \\\\x = \frac{-b \pm \sqrt{b^2 -4ac}}{2a}\\\\Substitute \ a, b, c \ in \ the \ equation.\\\\x = \frac{-b + \sqrt{b^2 -4ac}}{2a}, x =\frac{-b \ - \sqrt{b^2 -4ac}}{2a}\\\\x = \frac{8+ \sqrt{64 +14336}}{32}, x = \frac{8- \sqrt{64 +14336}}{32}\\\\x = \frac{8+ \sqrt{14400}}{32}, x = \frac{8-\sqrt{14400}}{32}\\\\x = \frac{8+120 }{32}, x= \frac{8-120}{32}\\\\x = \frac{128}{32} , x = \frac{-112}{32}\\\\x = 4 , x = \frac{-7}{2}\)
Since measure of length or width cannot be negative, we take x = 4
Solve the equation for u.
Uw + uq=r
Answers
Answer:
u = \(\frac{r}{w+q}\)
Step-by-step explanation:
Given
uw + uq = r ← factor out u from each term on the left side
u(w + q) = r ← divide both sides by (w + q)
u = \(\frac{r}{w+q}\)
The equation uw + uq = r is solved for u will be written as u = r / (w + q).
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.
The equation is given below.
uw + uq = r
Simplify the equation for u, then the equation will be written as,
uw + uq = r
u(w + q) = r
u = r / (w + q)
The equation uw + uq = r is solved for u will be written as u = r / (w + q).
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Use Green's Theorem to evaluate \( \int_{C} \sqrt{1+x^{3}} d x+2 x y d y \), where \( C \) is the triangle with vertices \( (0,0),(1,0) \) and \( (1,3) \)
Answers
The final result is \(0\). The triangle \(C\) is the region enclosed by the curve.
To evaluate the given line integral using Green's Theorem, we first need to find the vector field \(\mathbf{F} = \langle P, Q \rangle\) that corresponds to the integrand.
We have \(P(x, y) = \sqrt{1 + x^3}\) and \(Q(x, y) = 2xy\).
Next, we compute the partial derivatives of \(P\) and \(Q\) with respect to \(y\) and \(x\), respectively:
\(\frac{\partial P}{\partial y} = 0\) and \(\frac{\partial Q}{\partial x} = 2y\).
Now, we can apply Green's Theorem, which states that for a vector field \(\mathbf{F} = \langle P, Q \rangle\) and a simple closed curve \(C\) oriented counterclockwise,
\(\int_{C} P \, dx + Q \, dy = \iint_{D} \left(\frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y}\right) \, dA\),
where \(D\) is the region enclosed by \(C\).
In our case, the triangle \(C\) is the region enclosed by the curve. Let's denote this triangle as \(D\).
Using Green's Theorem, we have:
\(\int_{C} \sqrt{1+x^{3}} \, dx + 2xy \, dy = \iint_{D} \left(\frac{\partial (2xy)}{\partial x} - \frac{\partial (\sqrt{1+x^{3}})}{\partial y}\right) \, dA\).
Simplifying the partial derivatives, we have:
\(\int_{C} \sqrt{1+x^{3}} \, dx + 2xy \, dy = \iint_{D} (2y - 0) \, dA\).
Since the partial derivative with respect to \(y\) of the first term is zero, we only consider the second term.
Integrating \(2y\) with respect to \(A\) over \(D\), we get:
\(\int_{C} \sqrt{1+x^{3}} \, dx + 2xy \, dy = \iint_{D} 2y \, dA\).
To find the limits of integration for \(x\) and \(y\), we observe that the triangle \(D\) is bounded by the lines \(y = 0\), \(y = 3\), and \(x = 0\) to \(x = 1 - \frac{y}{3}\).
The integral becomes:
\(\int_{0}^{3} \int_{0}^{1 - \frac{y}{3}} 2y \, dx \, dy\).
Evaluating the inner integral first:
\(\int_{0}^{3} 2y\left[x\right]_{0}^{1 - \frac{y}{3}} \, dy\).
Simplifying:
\(\int_{0}^{3} 2y\left(1 - \frac{y}{3}\right) \, dy\).
Integrating:
\(\left[y^2 - \frac{1}{3}y^3\right]_{0}^{3}\).
Substituting the limits:
\(3^2 - \frac{1}{3}(3^3) - (0 - 0)\).
Simplifying:
\(9 - 9\).
The final result is \(0\).
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\(\(\int_{C} \sqrt{1+x^{3}} \, dx + 2xy \, dy = \iint_{D} 2y \, dA\).\)
Fun and integer that is between -8 and 5
Answers
Brayden stated that a flying disc had a circumference of 43.96 in. Eliza wanted to find the area of the same flying disc. What is the area of the flying disc rounded to the nearest whole number Both Brayden and Eliza used 3.14 for π
Answers
Answer:
153.86
Step-by-step explanation:
circumference: 43.96
43.96/3.14= 14 = diameter
14/2= 7 = radius
Area= 3.14(7)^2
= 3.14(49)
= 153.86
Evaluate the expression when x=3
, y=−4
, and z=−6
.
z−2xy=
z
−
2
x
y
=
Answers
The evaluation of the expression z − 2xy when x = 3, y = -4 and z = -6 is 18
How to evaluate the expressionFrom the question, we have the following parameters that can be used in our computation:
Expression: z − 2xy
Values: x = 3, y = -4 and z = -6
Substitute the known values in the above equation, so, we have the following representation
z − 2xy = -6 - 2 * 3 * -4
Evaluate the products
This gives
z − 2xy = -6 + 24
Evaluate the like terms in the equation
So, we have the following representation
z − 2xy = 18
Using the above as a guide, we have the following:
The solution is 18
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How do I do this I have gotten the first part which is B but it keeps saying it’s wrong when I put into calculator
Answers
Answer:
a. B is the correct equation
b. u = 5.8 sin(64°) = 5.2
Please help answer and explain am begging you
Answers
2,9 are negative
3,4,5,8 are undefined
Answer:
1.) positive
2.) negative
3.) zero
4.) undefined
5.) zero
6.) positive
7.) positive
8.) undefined
9.) negative
Question 31 (Essay Worth 5 points)
The position of an object at time t is given by s(t) = 1 - 12t. Find the instantaneous velocity at t = 2 by finding the derivative.
Answers
Answer:
-12
Step-by-step explanation:
ds/dt = d/dt ( 1-12 t)
ds/dt = -12
When t=2
ds/dt = -12
Refer to the picture framing problem. A new picture with the dimensions 25 in by 10 in will be framed with fancy that is 15 in by 10 in. What will be the dimensions of frame that will surround the picture? Show all work in finding the solution.
Answers
The difference between values is gotten by subtracting the values
The dimension of the frame that will surround the picture is 10 inches by 0 inches
How to determine the dimension of the pictureThe given parameters are:
Picture = 25 inches by 10 inchesFancy = 15 inches by 10 inchesThe dimension of the frame is the difference between the dimension of the fancy, and the picture.
So, we have:
Length = 25 inches - 15 inches
Length = 10 inches
Width = 10 inches - 10 inches
Width = 0 inches
Hence, the dimension of the frame that will surround the picture is 10 inches by 0 inches
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Emma puts $10,000$10,000 in a simple interest account at a bank. She will earn $1,800$1,800 in 44 years. What is the annual interest rate for the account?.
Answers
The annual interest rate for the account is, 4.5%.
What is simple interest?
Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.
Given:
I = Interest earned after t years = $1800
P = money invested = $10,000
t = length of time you invest = 4
r = annual rate of interest
We have to find the value of r.
Consider, the formula for simple interest
I = P x r x t
Plug the values of I, P, and t in the above equation,
1800 = 10,000 x r x 4
1800 = 40,000r
r = 1800 / 40,000
r = 0.045
r = 4.5%
Hence, the annual interest rate for the account is 4.5%.
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Given the following ANOVA table for three treatments each with six observations: df Mean square Source Treatment Error Total Sum of squares 1,122 1,074 2,196 What is the treatment mean square? Multiple Choice O 71.6 71.8 O O 561 537 a
Answers
The treatment mean square can be calculated by dividing the sum of squares for treatment by the degrees of freedom for treatment. In this case, the sum of squares for treatment is 1,122 and the degrees of freedom for treatment is 2. Therefore, the treatment mean square is 1,122/2 = 561. Therefore, the correct answer is: 561.
Based on the ANOVA table you've provided, you're interested in determining the treatment mean square. The treatment mean square (also called mean square between) is calculated by dividing the treatment sum of squares by the treatment degrees of freedom (df). Unfortunately, the ANOVA table appears to be incomplete, and I am unable to give you the specific numbers for the calculations.
However, I can guide you on how to calculate the treatment mean square. Once you have the treatment sum of squares and treatment df, simply follow this formula:
Treatment Mean Square = Treatment Sum of Squares / Treatment df
After applying this formula, you'll be able to choose the correct answer from the multiple-choice options you've mentioned: 71.6, 71.8, 561, or 537.
The treatment mean square can be calculated by dividing the sum of squares for treatment by the degrees of freedom for treatment. In this case, the sum of squares for treatment is 1,122 and the degrees of freedom for treatment is 2. Therefore, the treatment mean square is 1,122/2 = 561. Therefore, the correct answer is: 561.
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I don't understand.......
Answers
Answer:
Step-by-step explanation:
the dot is on the 32 and the line is the 3rd line
Are the ratios 1:20 and 2:4 equivalent?
Answers
Answer:
no
Step-by-step explanation:
Answer:
Simple answer, no.
attempts to classify a categorical outcome as a linear function of explanatory variables.a. Linear regressionb. Logistic regressionc. Supervised learningd. Classification mode
Answers
In this logistic regression equation, logit(pi) is the dependent or response variable and x is the independent variable.
The method that attempts to classify a categorical outcome as a linear function of explanatory variables is logistic regression. Logistic regression is a type of supervised learning in which a classification model is created to predict the probability of a binary outcome. It is often used when the outcome variable is dichotomous (e.g., yes/no, pass/fail) and the predictor variables are continuous or categorical. Linear regression, on the other hand, is used to model the relationship between a continuous outcome variable and one or more predictor variables.This type(logistic regression model) of statistical model (also known as logit model) is often used for classification and predictive analytics. Logistic regression estimates the probability of an event occurring, such as voted or didn’t vote, based on a given dataset of independent variables. Since the outcome is a probability, the dependent variable is bounded between 0 and 1. In logistic regression, a logit transformation is applied on the odds—that is, the probability of success divided by the probability of failure.Learn More About Logistic Regression: https://brainly.com/question/28391630
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A square has sides of length 6/12 inches. Area of length times width.
What is the area of the square in square inches?
Answers
The area of the square is 1/4inches² in square inches
What is area of squareThe area of a square is calculated by multiplying its two sides, that is area = s × s, where, 's' is one side of the square.
The square has side of length = 6/12
this can be simplified as 1/2
so
area of the square = (1/2 × 1/2) inches ²
area of the square = 1/4inches²
Thus, the area of the square is calculated using area = s × s, as 1/4inches²
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explain which properties of equality you used when solving the equation from part a to determine the mystery weight.
Answers
To solve the equation in part a and determine the mystery weight, we used the following properties of equality:
Addition property: This property states that if we add the same number to both sides of an equation, the equality is preserved. In this case, we added 23 grams to both sides of the equation to isolate the variable.
Subtraction property: This property states that if we subtract the same number from both sides of an equation, the equality is preserved. In this case, we subtracted 8 grams from both sides of the equation to isolate the variable.
Multiplication property: This property states that if we multiply both sides of an equation by the same number, the equality is preserved. In this case, we multiplied both sides of the equation by 3 to isolate the variable.
Division property: This property states that if we divide both sides of an equation by the same number (excluding 0), the equality is preserved. In this case, we divided both sides of the equation by 2 to isolate the variable.
By using these properties of equality, we were able to manipulate the equation and isolate the variable to determine the mystery weight.
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mike rides his motorcycle at an average speed of 60 miles per hour for 13 hour how far did he ride?
Answers
Step-by-step explanation:
speed = distance/time
therefore,
distance = speed × time
in our case
60 mph × 13 h = 780 miles
Mike rides his motorcycle at an average speed of 60 miles per hour for 13 hour 780 miles far did he ride.
To determine the distance.
We use speed formula which is
speed = distance/time
Given:
Mike rides his motorcycle at an average speed of 60 miles per hour for 13 hour,
Where Speed = 60 miles.
Time = 13 hour.
Pugging the values in speed formula.
speed = distance/time
60 = distance/13
distance = 60 * 13 = 780.
Therefore, The distance is 780 miles.
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Which one of these are Rational Numbers?
A) -7.9898...
B) 4.9832
C) 6.329...
D) 7
Answers
Answer:
D) 7
Step-by-step explanation:
The answer is D because A, B, and C are not considered numbers that are natural, whole, integers, or fractional. Irrational numbers are numbers that cannot be quantified any other way, do not have repeating decimals, and never end. A good example of this is π or 3.14159265.... you get the picture.
Hope this helps!
Edward deposited $8500 into a savings account 4 years ago. The simple interest rate is 5%. How much money did he earn in interest?
Answers
Step-by-step explanation:
bun the end of the yeah job. intend him dnd neer
t he held orlick knife David kamp jacory danforth Jackie renfrow quill lss Michael Kaepernick post Darvish Davydenko Comstock decision Nintendo Kuznetsov victory
8 to the power of 7 multiplied by 8 to the power of 3
Answers
8 to the power of 7 multiplied by 8 to the power of 3 = 8⁷ × 8³
8⁷ × 8³ = 8⁷⁺³ = 8¹⁰
Can someone help me with this pls?
Answers
Answer:
C. 7 ft
Step-by-step explanation:
I plugged it into a calculator
I hope this helps you
intro to geometric sequences (help pls)
Answers
Answer:
Option B
Step-by-step explanation:
The formula for geometric sequence is given by:
\(a_{n} = a_{1}r^{n-1}\)
Where,
\(a_{n}\) = nth term of sequence
\(a_{1}\) = 1st term of the sequence
\(r\) = common ratio (ration of the second term to the first term)
So,
Here:
\(a_{1}\) = 12
\(r\) = 6/12 = 1/2
Plugging in the values of \(a_{1}\) and r in the above formula:
=> \(a_{n} = 12 * (\frac{1}{2}) ^ {n-1}\)
What expressions are equivalent to 10^-5x10^2
Answers
See attachment for math work and answer.
what is 2,394x57,234
Answers
Explanation calculator